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Sibirskii Matematicheskii Zhurnal, 2016, Volume 57, Number 5, Pages 1114–1126
DOI: https://doi.org/10.17377/smzh.2016.57.517 (Mi smj2812) 		 
This article is cited in 7 scientific papers (total in 7 papers)

On some classes of inverse problems with overdetermination data on spatial manifolds

S. G. Pyatkovab

a Yugra State University, Khanty-Mansiisk, Russia
b Sobolev Institute of Mathematics, Novosibirsk, Russia
Full-text PDF (318 kB) Citations (7)
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DOI: https://doi.org/10.17377/smzh.2016.57.517
Abstract: We consider the question of well-posedness of the inverse problems of determining the righthand side (a source function) of a special form of a parabolic system of equations. The overdetermination data are the values of a solution and its normal derivatives on a system of surfaces in a spatial domain. In particular, the cross-sections of the domain can be used as these surfaces. Sharp conditions are presented for the data of the problem to ensure well-posedness.
Keywords: parabolic system, inverse problem, initial-boundary value problem, well-posedness, unconditional solvability.
Funding agency Grant number
Russian Foundation for Basic Research 15-41-00063
The author was supported by the Russian Foundation for Basic Research (Grant 15-41-00063).
Received: 02.10.2015
English version:
Siberian Mathematical Journal, 2016, Volume 57, Issue 5, Pages 870–880
DOI: https://doi.org/10.1134/S0037446616050177
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: S. G. Pyatkov, “On some classes of inverse problems with overdetermination data on spatial manifolds”, Sibirsk. Mat. Zh., 57:5 (2016), 1114–1126; Siberian Math. J., 57:5 (2016), 870–880
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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